Wh. Mulder, EQUILIBRIUM SIZE DISTRIBUTIONS OF CIRCULAR DOMAINS IN AMPHIPHILIC MONOLAYERS, JOURNAL OF PHYSICAL CHEMISTRY B, 101(39), 1997, pp. 7744-7750
An expression is derived for the free energy of a surfactant monolayer
at the interface between two immiscible bulk phases for a range of su
rface pressures in which two surface phases coexist. The condensed pha
se is assumed to be present in dispersed form, viz., as circular domai
ns embedded in the less dense phase. The domains are kept in fixed pos
itions as a result of electrostatic trapping. A thermodynamic analysis
is presented on the basis of the free energy expression for the case
of a single amphiphilic component using a mass-action equilibrium cond
ition, which yields the equilibrium distribution of domain sizes. The
distribution function is shown to be the result of a competition betwe
en a collective entropy effect (which favors dispersion), line tension
, electrostatic edge effects, and interdomain repulsion, while a possi
ble contribution due to bending elasticity of the phase boundary is ta
ken into account. A numerical example illustrates that for practical s
ystems the distributions are fairly narrow and that both the domain si
ze and the width of the distribution increases with the fractional sur
face coverage of the condensed phase, but in such a way that the degre
e of polydispersity decreases.